adjustment – Combination of adjusted parameters to create a variable and tell me the error it contains

Assuming you are using mathematica 12 (or higher),
it's pretty simple with the use Around, VectorAround, AroundReplace, etc.

Mathematica, in these versions, has an integrated error propagation:
So, you extract the covariance matrix and use AroundReplace
(he even uses the correlated error propagation)

So let's start: assuming your adjustment is in the variable fit:

covMat = fit("CovarianceMatrix");
bestParams = fit("BestFitParameters");
vecErr = bestParams((All, 1)) -> 
  VectorAround(bestParams((All, 2)), 0.5*(covMat + Transpose(covMat)))
AroundReplace(ArcTan(-b/a), vecErr)

the 0.5*(covMat + Transpose(covMat)) is used because the covariance matrix is ​​computed by a matrix inversion that is sometimes insufficiently stable to produce an absolute symmetric matrix that VectorAround will complain about. We therefore symmetry with force by hand.

He will even tell you what is the formula of your error if you plug symbols:

FullSimplify(
 AroundReplace(
  ArcTan(-b/a), {{a, b} -> 
    VectorAround({A, B}, {{C(A), C(A, B)}, {C(A, B), C(B)}})}), 
 A (Element) Reals && B (Element) Reals)

Release of AroundReplace symbolically

Numerical Methods – Elliptical Fourier Adjustment Coefficients

I'm trying to implement a function that could correspond to an elliptic Fourier curve on a set of border points of a detected object. I use cv2.findContours to acquire border points from a binary image. Then I would like to calculate the elliptic Fourier coefficients using the equation:

(for the sake of simplicity, I will only discuss the x-axis)

here is the equation:

the coefficients

And here is my question:
The idea is to set the x coordinates from 0 to 2 * π. My question is: if Δt should be a constant or should it depend on Δx (the greater the change in x-coordinate, the larger the Δt)?

8 – adjustment / testing of PHP memory

I'm running a Drupal 8 site and I'm not 100% sure of the amount of ideal PHP memory. I would like to try to experiment with different memory options.

The environment does not allow me to restart Apache on the fly. Could I just go to the settings.php file and change the ini_set() calls to define different options and see how it behaves?

usa – Renunciation available for abandoning status adjustment

I need help on the type of waiver that can help my situation. I arrived in the United States in 2016 with a visitor visa and I married a US citizen in 2017 and we filed the application for a change of status in 2018. Although the procedure is still pending, I am I had to deal with an emergency and country without early parole. I have exceeded my visa for more than a year before applying to the OSA.
My wife and I are looking for ways to bring me home

I will appreciate all the advice.

Adjustment of two-dimensional data

For this question, I can not use random sample data. So the actual data can be found here. The data file contains three columns, the first two being the coordinates $ (x, y) $, while the third is the value of a function $ f $. Now we are tracing them, thus getting the form of $ f $

data = Import["L1.dat", "Table"]; 

or

data = Import["https://pastebin.com/raw/YMCFB4mK", "TSV"]

Ground

L0 = ListPlot3D[data]

enter the description of the image here

My question is this: Is there a way to interpolate the data and get an analytic fit function? $ f (x, y) $? Given the fact that the distribution of $ f $ is rather smooth, with no picks and no holes, I guess it should be pretty easy to get its adjustment function. Ideas?

layout – Visual adjustment of the information contained in a map

The context

Currently I am working on the product list page of an online store. The products presented on the online store can in principle be rented and we have set rental prices for different durations, such as monthly, weekly, daily, hourly and minute prices.
If the store owner has set all these prices, we must display them all in the product card.

The current map looks like this:

enter the description of the image here

Since I am involved in redesigning the online store, I wanted to change the look and feel of the product cards so that I could insert more cards in a row and display the visual information correctly.

This is what I mocked:

enter the description of the image here

Problem

In the redesigned model, we can see that only the first three price breakdowns are visible. I want to show the rental prices that are at the hour and the minute. For that, I need an extra horizontal space.

What I had in mind was to introduce a carousel inside the card in the price section, which would display the two remaining prizes. Will it be a good ux model?

Something like that:

enter the description of the image here

Let me know what you think about this scheme and any alternative we could introduce for such a case. Thank you !!

adjustment – partial and partial partial correlation

Mathematica has a Partial correlation function, but it's for the chronological data. However, by following the Partial and Partial Partial Correlation information, you can use simple methods. Mathematica orders.

(* The data *)
SATV = {500, 550, 450, 400, 600, 650, 700, 550, 650, 550};
HSGPA = {3.0, 3.2, 2.8, 2.5, 3.2, 3.8, 3.9, 3.8, 3.5, 3.1};
FGPA = {2.8, 3.0, 2.8, 2.2, 3.3, 3.3, 3.5, 3.7, 3.4, 2.9};
data = Transpose[{SATV, HSGPA, FGPA}];

(* Find residues for both regressions on SATV *)
resid1 = LinearModelFit[data[[All, {1, 2}]], x, x]["FitResiduals"];
resid2 = LinearModelFit[data[[All, {1, 3}]], x, x]["FitResiduals"];

(* Partial correlation *)
Correlation[resid1, resid2]
(* 0.7475739092548284 *)

(* Semi-partial correlation *)
Correlation[FGPA, resid1]
(* 0.43378526772255077 *)

The results correspond exactly to the R example in the link above.

plot – adjustment problem

I'm trying to find an appropriate matching function for the following dataset:

xyzValues ​​= Import["nC_Q4.csv", "Data"][[8 ;;, {6, 9, 38}]]{{0, 0, 2.0004}, {0, 100, 0}, {0, 40, 0}, {0, 140, 0}, {0, 60, 0}, {0,
80, 0}, {0, 120, 0}, {0, 20, 0}, {0, 160, 0}, {0, 180, 0}, {0, 240,
0}, {0, 220, 0}, {0, 200, 0}, {0, 260, 0}, {0, 280, 0}, {0, 300,
0}, {0, 320, 0}, {0, 340, 0}, {0, 360, 0}, {0, 400, 0}, {0, 380,
0}, {0, 440, 0}, {0, 420, 0}, {0, 460, 0}, {5, 0, 1,1607}, {5, 20,
0}, {5, 40, 0}, {5, 60, 0}, {5, 80, 0}, {5, 100, 0}, {O, 480,
0}, {0, 500, 0}, {5, 120, 0}, {5, 140, 0}, {5, 160, 0}, {5, 180,
0}, {5, 200, 0}, {5, 240, 0}, {5, 220, 0}, {5, 260, 0}, {5, 280,
0}, {5, 300, 0}, {5, 320, 0}, {5, 340, 0}, {5, 360, 0}, {5, 380,
0}, {5, 400, 0}, {5, 420, 0}, {10, 20, 0}, {5, 440, 0}, {10, 0,
0.480288}, {5, 460, 0}, {10, 60, 0}, {5, 480, 0}, {5, 500, 0}, {10,
40, 0}, {10, 80, 0}, {10, 100, 0}, {10, 120, 0}, {10, 140, 0}, {10,
160, 0}, {10, 180, 0}, {10, 200, 0}, {10, 220, 0}, {10, 240,
0}, {10, 260, 0}, {10, 280, 0}, {10, 300, 0}, {10, 320, 0}, {10,
340, 0}, {10, 360, 0}, {10, 380, 0}, {10, 400, 0}, {10, 420,
0}, {10, 460, 0}, {10, 480, 0}, {10, 440, 0}, {15, 0, 0.5003}, {10,
500, 0}, {15, 20, 0}, {15, 40, 0}, {15, 60, 0}, {15, 100, 0}, {15,
80, 0}, {15, 120, 0}, {15, 140, 0}, {15, 160, 0}, {15, 180, 0}, {15,
200, 0}, {15, 220, 0}, {15, 240, 0}, {15, 260, 0}, {15, 280,
0}, {15, 300, 0}, {15, 320, 0}, {15, 340, 0}, {15, 360, 0}, {15,
380, 0}, {15, 400, 0}, {15, 420, 0}, {15, 460, 0}, {15, 440,
0}, {15, 480, 0}, {15, 500, 0}, {20, 0, 0.520104}, {20, 20, 0}, {20,
40, 0}, {20, 60, 0}, {20, 80, 0}, {20, 100, 0}, {20, 120, 0}, {20,
140, 0}, {20, 160, 0}, {20, 180, 0}, {20, 200, 0}, {20, 220,
0}, {20, 240, 0}, {20, 260, 0}, {20, 280, 0}, {20, 300, 0}, {20,
320, 0}, {20, 340, 0}, {20, 360, 0}, {20, 380, 0}, {20, 400,
0}, {20, 420, 0}, {20, 440, 0}, {20, 460, 0}, {20, 480, 0}, {20,
500, 0}, {25, 0, 0.980392}, {25, 20, 0}, {25, 40, 0}, {25, 80,
0}, {25, 60, 0}, {25, 100, 0}, {25, 120, 0}, {25, 140, 0}, {25, 160,
0}, {25, 180, 0}, {25, 200, 0}, {25, 220, 0}, {25, 240, 0}, {25,
260, 0}, {25, 280, 0}, {25, 300, 0}, {25, 320, 0}, {25, 340,
0}, {25, 360, 0}, {25, 380, 0}, {25, 400, 0}, {25, 420, 0}, {25,
440, 0}, {25, 480, 0}, {25, 460, 0}, {25, 500, 0}, {30, 0,
2,36047}, {30, 20, 0}, {30, 40, 0}, {30, 60, 0}, {30, 80, 0}, {30,
100, 0}, {30, 120, 0}, {30, 140, 0}, {30, 160, 0}, {30, 180,
0}, {30, 200, 0}, {30, 220, 0}, {30, 240, 0}, {30, 260, 0}, {30,
280, 0}, {30, 300, 0}, {30, 320, 0}, {30, 340, 0}, {30, 360,
0}, {30, 380, 0}, {30, 400, 0}, {30, 420, 0}, {30, 440, 0}, {30,
460, 0}, {30, 480, 0}, {30, 500, 0}, {35, 0, 14.943}, {35, 20,
0}, {35, 40, 0}, {35, 60, 0}, {35, 80, 0}, {35, 100, 0}, {35, 120,
0}, {35, 140, 0}, {35, 160, 0}, {35, 180, 0}, {35, 200, 0}, {35,
220, 0}, {35, 240, 0}, {35, 260, 0}, {35, 280, 0}, {35, 300,
0}, {35, 320, 0}, {35, 340, 0}, {35, 360, 0}, {35, 380, 0}, {35,
400, 0}, {35, 420, 0}, {35, 440, 0}, {35, 460, 0}, {35, 480,
0}, {35, 500, 0}, {40, 0, 28.6972}, {40, 20, 0}, {40, 40, 0}, {40,
60, 0}, {40, 80, 0}, {40, 100, 0}, {40, 120, 0}, {40, 140, 0}, {40,
160, 0}, {40, 180, 0}, {40, 200, 0}, {40, 220, 0}, {40, 240,
0}, {40, 260, 0}, {40, 280, 0}, {40, 320, 0}, {40, 300, 0}, {40,
340, 0}, {40, 360, 0}, {40, 380, 0}, {40, 400, 0}, {40, 420,
0}, {40, 440, 0}, {40, 460, 0}, {40, 480, 0}, {40, 500, 0}, {45, 0,
34.7878}, {45, 20, 0}, {45, 40, 0}, {45, 60, 0}, {45, 80, 0}, {45,
100, 0}, {45, 120, 0}, {45, 140, 0}, {45, 160, 0}, {45, 180,
0}, {45, 200, 0}, {45, 220, 0}, {45, 240, 0}, {45, 260, 0}, {45,
280, 0}, {45, 300, 0}, {45, 320, 0}, {45, 340, 0}, {45, 360,
0}, {45, 380, 0}, {45, 400, 0}, {45, 420, 0}, {45, 440, 0}, {45,
460, 0}, {45, 480, 0}, {45, 500, 0}, {50, 0, 39, 7718}, {50, 20,
0}, {50, 40, 0}, {50, 60, 0}, {50, 80, 0}, {50, 100, 0}, {50, 120,
0}, {50, 140, 0}, {50, 160, 0}, {50, 180, 0}, {50, 200, 0}, {50,
220, 0}, {50, 260, 0}, {50, 240, 0}, {50, 280, 0}, {50, 300,
0}, {50, 320, 0}, {50, 340, 0}, {50, 360, 0}, {50, 380, 0}, {50,
400, 0}, {50, 420, 0}, {50, 440, 0}, {50, 460, 0}, {50, 480,
0}, {50, 500, 0}, {55, 0, 47.2884}, {55, 20, 0}, {55, 40, 0}, {55,
60, 0}, {55, 80, 0}, {55, 100, 0}, {55, 120, 0}, {55, 140, 0}, {55,
160, 0}, {55, 180, 0}, {55, 200, 0}, {55, 220, 0}, {55, 240,
0}, {55, 260, 0}, {55, 280, 0}, {55, 300, 0}, {55, 320, 0}, {55,
340, 0}, {55, 360, 0}, {55, 400, 0}, {55, 380, 0}, {55, 420,
0}, {55, 440, 0}, {55, 460, 0}, {55, 480, 0}, {55, 500, 0}, {60, 0,
62.3125}, {60, 20, 0.22022}, {60, 40, 0}, {60, 60, 0}, {60, 80,
0}, {60, 100, 0}, {60, 120, 0}, {60, 140, 0}, {60, 160, 0}, {60,
180, 0}, {60, 200, 0}, {60, 220, 0}, {60, 240, 0}, {60, 260,
0}, {60, 280, 0}, {60, 300, 0}, {60, 320, 0}, {60, 340, 0}, {60,
360, 0}, {60, 380, 0}, {60, 400, 0}, {60, 420, 0}, {60, 460,
0}, {60, 440, 0}, {60, 480, 0}, {60, 500, 0}, {65, 0, 74, 2594}, {65,
20, 0.26026}, {65, 40, 0.020016}, {65, 60, 0}, {65, 80, 0}, {65,
100, 0}, {65, 120, 0}, {65, 140, 0}, {65, 160, 0}, {65, 180,
0}, {65, 200, 0}, {65, 220, 0}, {65, 240, 0}, {65, 260, 0}, {65,
280, 0}, {65, 300, 0}, {65, 320, 0}, {65, 340, 0}, {65, 360,
0}, {65, 380, 0}, {65, 400, 0}, {65, 420, 0}, {65, 440, 0}, {65,
460, 0}, {65, 480, 0}, {65, 500, 0}, {70, 0, 79, 459}, {70, 20,
1.60128}, {70, 40, 0.0800641}, {70, 60, 0.020004}, {70, 80, 0}, {70,
100, 0}, {70, 140, 0}, {70, 120, 0}, {70, 160, 0}, {70, 200,
0}, {70, 180, 0}, {70, 220, 0}, {70, 240, 0}, {70, 260, 0}, {70,
280, 0}, {70, 320, 0}, {70, 300, 0}, {70, 340, 0}, {70, 360,
0}, {70, 380, 0}, {70, 400, 0}, {70, 420, 0}, {70, 440, 0}, {70,
460, 0}, {70, 480, 0}, {70, 500, 0}, {75, 0, 86.9348}, {75, 20,
7.30146}, {75, 40, 1.96196}, {75, 60, 0.720144}, {75, 80,
0.46046}, {75, 100, 0.160096}, {75, 120, 0.080016}, {75, 140,
0.020008}, {75, 160, 0.020008}, {75, 180, 0.020012}, {75, 200,
0.020012}, {75, 220, 0.020012}, {75, 240, 0}, {75, 260, 0}, {75,
300, 0}, {75, 280, 0}, {75, 320, 0}, {75, 340, 0}, {75, 360,
0}, {75, 380, 0}, {75, 400, 0}, {75, 420, 0}, {75, 440, 0}, {75,
460, 0}, {75, 480, 0}, {75, 500, 0}, {80, 0, 91.4783}, {80, 20,
13.1653}, {80, 40, 7.70308}, {80, 80, 4.0208}, {80, 60,
5.48439}, {80, 120, 2,84114}, {80, 100, 3.22064}, {80, 140,
2,60104}, {80, 160, 1,80216}, {80, 180, 1,86037}, {80, 200,
1,36054}, {80, 220, 1.24149}, {80, 240, 1.08065}, {80, 260,
1,04021}, {80, 280, 0.960384}, {80, 300, 0.860861}, {80, 320,
1.0004}, {80, 340, 0.80016}, {80, 360, 0.720432}, {80, 380,
0.540432}, {80, 400, 0.480673}, {80, 420, 0.40032}, {80, 440,
0.20008}, {80, 480, 0.380076}, {80, 460, 0.460184}, {80, 500,
0.460276}, {85.0, 94.2188}, {85, 20, 22.0332}, {85, 40,
12.2649}, {85, 60, 9.26371}, {85, 80, 7.78156}, {85, 100,
7.14572}, {85, 120, 5.84117}, {85, 140, 5.58447}, {85, 180,
4.90196}, {85, 160, 5.32106}, {85, 200, 4.5209}, {85, 220,
4.5209}, {85, 240, 4.74095}, {85, 260, 4.18167}, {85, 280,
3.80076}, {85, 300, 3.92392}, {85, 320, 3.72223}, {85, 340,
3.64073}, {85, 360, 3.38068}, {85, 380, 3.5007}, {85, 400,
3.36336}, {85, 420, 3.14126}, {85, 440, 3.02181}, {85, 460,
2,70054}, {85, 480, 3.02242}, {85, 500, 2.90174}, {90, 0,
95.7592}, {90, 20, 33, 13333}, {90, 60, 18, 1709}, {90, 40,
22.1689}, {90, 80, 15.8358}, {90, 100, 13.9856}, {90, 120,
12.7826}, {90, 140, 12.0272}, {90, 160, 10.024}, {90, 180,
10.8643}, {90, 200, 9.60192}, {90, 220, 8.80528}, {90, 240,
8.30332}, {90, 260, 8.64173}, {90, 280, 7.74465}, {90, 300,
7.40148}, {90, 320, 7.92317}, {90, 340, 7.48899}, {90, 360,
6.7427}, {90, 380, 6.82546}, {90, 400, 6.2425}, {90, 420,
6,76135}, {90, 440, 6, 40512}, {90, 460, 6.84137}, {90, 480,
5.54222}, {90, 500, 6.16246}, {95, 0, 97.4795}, {95, 20,
42.9972}, {95, 40, 31.8191}, {95, 60, 28.6657}, {95, 80,
25.6903}, {95, 100, 22.8337}, {95, 120, 21.733}, {95, 140,
20.1201}, {95, 160, 18, 6074}, {95, 180, 18.6875}, {95, 200,
17.3635}, {95, 220, 17.1869}, {95, 240, 16.6433}, {95, 260,
15.6062}, {95, 280, 15.3954}, {95, 300, 14.8118}, {95, 320,
15.3985}, {95, 340, 14, 1657}, {95, 360, 14.9439}, {95, 380,
14.5229}, {95, 400, 14.0684}, {95, 420, 13.5681}, {95, 440,
13.4454}, {95, 460, 12.7051}, {95, 480, 13.5227}, {100, 0,
98.3397}, {95, 500, 13.2653}, {100, 20, 52.0416}, {100, 40,
43.1773}, {100, 60, 38.2153}, {100, 80, 34.9079}, {100, 100,
32.0328}, {100, 120, 30.5506}, {100, 140, 29.3729}, {100, 160,
29.0407}, {100, 180, 27.0908}, {100, 200, 26.4853}, {100, 220,
25.8252}, {100, 240, 25.245}, {100, 280, 24, 1697}, {100, 260,
25.4152}, {100, 300, 25.2752}, {100, 320, 22.8646}, {100, 340,
23.0246}, {100, 360, 22.0888}, {100, 380, 22.2467}, {100, 400,
23.3247}, {100, 420, 22.9892}, {100, 440, 21.0242}, {100, 460,
20.9284}, {100, 480, 21.8775}, {100, 500, 19,6035}}

Who has dimensions

Dimensions[xyzValues]

{546, 3}

First, I tried to draw these points in a contour plot:

ListContourPlot[xyzValues, PlotLegends -> Automatic, 
 ColorFunction -> "Rainbow", PlotRange -> {{0, 100}, {0, 150}}]

enter the description of the image here

but this result does not reflect the data points (see, for example, data in the empty area of ​​the plot). I'm probably missing something, but the plot should be different.
Draw these points with another mathematical framework:

enter the description of the image here

Looking at these two graphs, I do not know how to compute a good math function to match that data point. I made an approximation

model = a + b x + c x ^ 2 + Exp[-x] + e y + f y ^ 2 + g x y + Exp[-y] h;

fit =
FindFit[xyzValues, model, {a, b, c, d, e, f, g, h}, {x, y}]

{a -> -2.75705, b -> -0.196263, c -> 0.00570384,
d -> -4.9015, e -> 0.0131326, f -> 0.0000346097, g -> -0.000773403,
h -> 38,7327}

and plot this function:

Show[{Plot3D[Evaluate[model /. fit], {x, 0, 100}, {y, 0, 150},
Plot Style -> Opacity[0.8]],
Graphics3D[{Red, PointSize[.025], Map[Point, xyzValues]}]}]

enter the description of the image here

However, this seems to be an approximation with a lot of error. I would like to get a function with less error, if possible an expression that interpolates from data points.

cordially

5th dnd – Is this homebrew spiritual inquiry spell an adjustment of Talking to Death to be lower level, balanced as a 1st level spell?

I have the impression that necromancers have few under-death episodes below the 3rd level. Only necrotic damage. I wanted to change that.

It's relatively simple to extrapolate spell levels for spells like fireball and hot hands, both because of the "at higher levels" section of the spell and because you can compare existing spells when determining damage, it's not easy with spells like talk with dead people.

Speak with the dead does not offer options for the upper and lower levels, and I think this is because the ability to ask open questions is powerful enough that even with 1 or 2 questions, it is only 39, a gimme at lower levels. That being said, I think I have found a way to limit this:

Spiritual inquiry

Necromancy of 1st level

Casting time: 1 action

Interval: 10 feet

components: V, S, M (burning incense)

duration: 1 minute

You reach the spirit of a corpse at hand, allowing it to answer a single question yes or no. The corpse must still have a mouth and can not be undead. The spell fails if the corpse was the target of this spell or talk with dead people in the last 10 days.

Until the end of the spell, you can ask the corpse a question to which he can answer only by "yes", "no" or "I do not know". The corpse only knows what he has known in life, including the languages ​​that he knew. The corpse is not obliged to give you a truthful answer if you are hostile or it recognizes you as an enemy. This spell does not bring back the soul of the creature in his body, but only in his animating spirit. Thus, the corpse can not learn new information, understands nothing that has happened since his death and can not speculate on future events.

Is the 1st level appropriate for this spell? If not, what makes it too strong or too weak?

phase detection – How does automatic AF adjustment work?

One of my answers has been changed to include automatic autofocus (AFMA) adjustment as a camera selection criterion. The change related to another response further explaining the AFMA.

My understanding of autofocus is:

  • Autofocus is closed loop if contrast detection is used. AFMA should therefore not be necessary for autofocus because the focus is confirmed in the contrast detection autofocus at the imaging sensor.
  • Open-loop AF, such as phase-detection AF, calculates the predefined focus adjustment based on the current position and the predicted optimal position. Thus, if it does not work, its amplitude depends on the current position of the focus.

So, my questions are:

  • Is AFMA a goal or a global adjustment?
  • Can AFMA really correct the problems associated with low focus lens / housing combinations?
  • What is the AFMA adjustment? Is it an additive shift between the intended position and the actually chosen position? Or is it a multiplicative correction of the amount of focus?
  • Is AFMA used for autofocus with contrast detection? Is it used for Canon's dual-pixel autofocus?
  • How can AFMA operation work if the operation of the AF system depends on the current focus position? I mean, if focus does not work, should not the reduction depend on the current focus position? So, if you shoot an object / person at 2 meters, the current focus position is at 1 meter, which is different from what it would be if the current focus position was at the ## EQU1 ## 39; infinity.

In my opinion, if AFRA takes advantage of the optical distance between the phase-detection autofocus sensor and the phase-detection autofocus sensor and the optical image sensor, the additional shift can be beneficial. Is this why AFMA is used? So, I basically mean that the focus on the PDAF sensor is not the same as the focus on the imaging sensor.